This is among the many questions haunting businesses as they scramble to protect themselves from a constant barrage of domestic and foreign cyberattacks. What's at stake to businesses and the governments they work with in this high-tech warfare is nothing less than the nation's economic security.

As part of CNBC's ongoing special "Hacking America", we're asking top CEOs and cybersecurity experts about the potential damage of cyberattacks, and what businesses and governments can do to protect themselves—and you.

At the IHS CERAWeek Conference in Houston on Wednesday, CNBC spoke to BP CEO Bob Dudley about the persistent cyberthreats that companies like his receive.

"Cybersecurity is a growing issue around the world, not only with companies but with governments," Dudley observed. "We see as many as 50,000 attempts a day like many big companies … to my knowledge we haven't had an incident that's taken away data from us, but we're incredibly vigilant."